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Topic: Number of lattice paths with given steps?
Replies: 7   Last Post: Nov 24, 2012 6:41 AM

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William Elliot

Posts: 1,606
Registered: 1/8/12
Re: Number of lattice paths with given steps?
Posted: Nov 20, 2012 11:01 PM
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On Tue, 20 Nov 2012, IV wrote:

> I'm looking for a formula for calculating the number of lattice paths in a
> rectangular quadratic integer lattice with given kind of steps and given
> numbers of steps of each kind.


What's a rectangular quadratic integer lattice?

Is it, by some far fetched possibility, Z^2 with the product
order, ie (j,k) <= (n,m) when j <= n, k <= m. Or do you
simply mean Z^2 with no lattice order?

I suppose are there four kinds of steps, up, down, left, right
and if some steps are missing, tough.

Now what the heck is a lattice path? Any finite path.
Any finite path from a point?
Any finite path from a point to another given point?

> That means all lattice paths with n1 steps (1,1), n2 steps (1,2), n3
> steps (1,3) and so on - the numbers n1, n2, n3, ... are given.
>

What constitutes the step (1,2)?

> Can somebody help?
>

I'm dubious as you wright stream of conscious nonsense comprehensible
only by mind readers who refrain from reading your reprehensible mind.

> Was this problem already discussed in the literature?



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